Skip to main content
Log in

Chemotherapy appointment scheduling and daily outpatient–nurse assignment

  • Published:
Health Care Management Science Aims and scope Submit manuscript


Chemotherapy planning and patient–nurse assignment problems are complex multiobjective decision problems. Schedulers must make upstream decisions that affect daily operations. To improve productivity, we propose a two-stage procedure to schedule treatments for new patients, to plan nurse requirements, and to assign the daily patient mix to available nurses. We develop a mathematical formulation that uses a waiting list to take advantage of last-minute cancellations. In the first stage, we assign appointments to the new patients at the end of each day, we estimate the daily requirement for nurses, and we generate the waiting list. The second stage assigns patients to nurses while minimizing the number of nurses required. We test the procedure on realistically sized problems to demonstrate the impact on the cost effectiveness of the clinic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others


  1. Le cancer.

  2. Interview with members of the managerial team at the chemotherapy clinic of Notre-Dame hospital. Personal communication (2016)

  3. Alvarado M, Ntaimo L (2016) Chemotherapy appointment scheduling under uncertainty using mean-risk stochastic integer programming. Health Care Management Science.

    Article  Google Scholar 

  4. Berwick DM, Nolan TW, Whittington J (2008) The triple aim: care, health, and cost. Health Aff 27 (3):759–769

    Article  Google Scholar 

  5. Condotta A, Shakhlevich N (2014) Scheduling patient appointments via multilevel template: a case study in chemotherapy. Oper Res Health Care 3(3):129–144

    Article  Google Scholar 

  6. Dobish R (2003) Next-day chemotherapy scheduling: a multidisciplinary approach to solving workload issues in a tertiary oncology center. J Oncol Pharm Pract 9(1):37–42

    Article  Google Scholar 

  7. Gocgun Y, Puterman ML (2014) Dynamic scheduling with due dates and time windows: an application to chemotherapy patient appointment booking. Health Care Manag Sci 17(1):60–76

    Article  Google Scholar 

  8. Green E, Preyra C, Stewart J, McLennan C, Bland R, Dus T, Langhorn M, Beattie K, Cheung A, Hertz S, Sechter H, Burns J, Angus H, Sawka C (2012) . Determining resource intensity weights in ambulatory chemotherapy related to nursing workload 22:114–28

    Google Scholar 

  9. Hahn-Goldberg S, Carter MW, Beck JC (2012) Dynamic template scheduling to address uncertainty in complex scheduling problems: a case study on chemotherapy outpatient scheduling. In: Society for health systems conference. Las Vegas

  10. Lamé G, Jouini O, Stal-Le Cardinal J (2016) Outpatient chemotherapy planning: a literature review with insights from a case study. IIE Trans Healthcare Syst Eng 6(3):127–139

    Article  Google Scholar 

  11. Liang B, Turkcan A, Ceyhan ME, Stuart K (2015) Improvement of chemotherapy patient flow and scheduling in an outpatient oncology clinic. Int J Prod Res 53(24):7177–7190

    Article  Google Scholar 

  12. Sadki A, Xie X, Chauvin F (2010) Patients assignment for an oncology outpatient unit. In: 2010 IEEE Conference on automation science and engineering (CASE). IEEE, pp 891– 896

  13. Sadki A, Xie X, Chauvin F (2011) Appointment scheduling of oncology outpatients. In: 2011 IEEE Conference on automation science and engineering (CASE). IEEE, pp 513–518

  14. Santibáñez P, Aristizabal R, Puterman ML, Chow VS, Huang W, Kollmannsberger C, Nordin T, Runzer N, Tyldesley S (2012) Operations research methods improve chemotherapy patient appointment scheduling. Joint Commission J Qual Patient Safe 38(12):541–553

    Article  Google Scholar 

  15. Turkcan A, Zeng B, Lawley M (2012) Chemotherapy operations planning and scheduling. IIE Trans Healthcare Syst Eng 2(1): 31–49

    Article  Google Scholar 

  16. Van Merode GG, Groothuis S, Schoenmakers M, Boersma HH (2002) Simulation studies and the alignment of interests. Health Care Manag Sci 5(2):97–102

    Article  Google Scholar 

  17. Wong Kee Yan N (2017) Chemotherapy outpatient scheduling at the Segal Cancer Center using mixed integer programming models. Ph.D. thesis, Concordia University

  18. Woodall JC, Gosselin T, Boswell A, Murr M, Denton BT (2013) Improving patient access to chemotherapy treatment at Duke Cancer Institute. Interfaces 43(5):449–461

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Nadia Lahrichi.


Appendix A: Measure of hourly workload (\({G^{p}_{i}}\))

The CTC prepared a list of rules related to workload balancing. We use it to develop two parameters to facilitate the estimation of workload. The first, \({G^{p}_{i}}\) (Table 9), represents the hourly workload that the patient requires.

Table 9 Hourly workload associated with each type of task, \({G^{p}_{i}}\)

Appendix B: Linearization of the formulation

Constraints (1l) and (1m) are both nonlinear. We use a big-M approach to linearize them: Constraints (4a) and (4b) replace (1l), and Constraints (4c) and (4d) replace (1m). The parameter \({\Theta }_{i^{p}}\) plays the role of the big M; it is tightened as much as possible in each case.

$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \left( \sum\limits_{j \in J} j x^{p}_{(i-1)j}+a^{p}_{(i-1),i}\right)\\ -\sum\limits_{j \in J} j x^{p}_{ij}\leq \left( 1-{y^{p}_{i}}\right){{\Theta}^{p}_{i}} \\ \quad\forall i \in \{I^{p}| i > 1\}, \forall p\in P \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{j \in J} j x^{p}_{ij} \leq \sum\limits_{j \in J} j x^{p}_{(i-1)j}+a^{p}_{(i-1),i}\\ \quad \forall i \in \{I^{p}| i > 1\}, \forall p\in P \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{h \in H} h \sum\limits_{j\in J}u^{p}_{(i-1)jh}-\sum\limits_{h\in H} h \sum\limits_{j \in J}u^{p}_{ijh}\leq \\ \left( 1-{y^{p}_{i}}\right)|H| \quad \forall i \in \{I^{p}| i > 1\}, \forall p\in P \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{h \in H} h \sum\limits_{j \in J}u^{p}_{ijh} \leq \sum\limits_{h \in H} h \sum\limits_{j \in J}u^{p}_{(i-1)jh}\\ \quad \forall i \in \{I^{p}| i > 1\}, \forall p\in P \end{array} \end{array} $$

Appendix C: Formulation of offline model



1 if treatment ip of patient p is assigned to nurse f on day j in time slot h; 0 otherwise


1 if treatment ip of patient p is assigned; 0 otherwise


1 if nurse f is assigned; 0 otherwise


1 if nurse f is on break in time slot h; 0 otherwise


Integer variable: number of tasks handled, {0...E}


Integer variable: first overflow level, {0...B}


Integer variable: second overflow level, {0...C}


$$ \begin{array}{lllllllllll} min \sum\limits_{f\in F\setminus\{virtual\}}\sum\limits_{j\in J}\eta z_{fj}+\alpha \tau_{fj} +\beta \sigma_{fj} + \gamma \iota_{fj} \\ + \epsilon \sum\limits_{p\in P}\sum\limits_{i^{p}\in i^{p}}\sum\limits_{j\in J}\sum\limits_{h\in H} x^{p}_{i(virtual)jh} \end{array} $$


$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{p\in P}\sum\limits_{i\in I^{p}}\sum\limits_{f\in F}\sum\limits_{h^{\prime}=max(1,h + 1 -{D^{p}_{i}})}^{min(h,H + 1-{D^{p}_{i}})}L^{p}_{li} x^{p}_{ifjh^{\prime}}\leq \\ V_{l} \quad \forall j\in PP, \forall h \in H, \forall l \in L \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{f\in F}\sum\limits_{j\in PP}\sum\limits_{h\in H} h x^{p}_{ifjh}+{D^{p}_{i}}\leq |H| \\ \quad \forall i\in I^{p}, \forall p \in P \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{p\in P}\sum\limits_{i\in i^{p}}\sum\limits_{h^{\prime}=max(1,h + 1-{D^{p}_{i}})}^{min(h,H + 1-{D^{p}_{i}})} {G^{p}_{i}} x^{p}_{ijfh^{\prime}}\leq N \\ \quad \forall f \in F\setminus\{virtual\}, \forall j \in PP, \forall h \in H \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{p\in P}\sum\limits_{i\in I^{p}}\sum\limits_{h \in H} {W^{p}_{i}} x^{p}_{ifjh^{\prime}}\leq W \\ \quad \forall f \in F, \forall j\in PP, \forall h \in H \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{p\in P} \sum\limits_{i\in I^{p}} x^{p}_{ifjh}\leq 1\\ \quad \forall f \in F\setminus\{virtual\},\forall j \in PP, \forall h \in H \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{p\in P}\sum\limits_{i\in i^{p}}\sum\limits_{h\in H} P^{p}_{ai} x^{p}_{ifjh}\leq M_{a} \\ \quad \forall f \in F\setminus\{virtual\},\forall j\in PP, \forall a \in A \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} a^{p} \leq \sum\limits_{j\in PP} \sum\limits_{h \in H}j x^{p}_{1fjh}\leq b^{p}\quad \forall p\in P \end{array} $$
$$\begin{array}{@{}rcl@{}} {y^{p}_{i}} \leq y^{p}_{(i-1)} \quad \forall i \in \{I^{p}| i > 1\}, \forall p\in P \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} {y^{p}_{i}} \left( \sum\limits_{j\in PP} j x^{p}_{ifjh} -\sum\limits_{j\in PP} j x^{p}_{(i-1)fjh}\right)\\ = {y^{p}_{i}} a^{p}_{(i-1),i} \quad \forall i \in \{I^{p}| i > 1\}, \forall p\in P \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} v_{fjh}+v_{fj(h + 2)}+v_{fj(h + 4)} = z_{fj} \\ \quad h={7},\forall f \in F\setminus\{virtual\}, \forall j \in PP \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} v_{fjh}+v_{fj(h + 2)}+v_{fj(h + 4)} = z_{fj} \\ \quad h={8},\forall f \in F\setminus\{virtual\},\forall j \in PP \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} h v_{fjh}+(h + 2) v_{fj(h + 2)}\\ +(h + 4) v_{fj(h + 4)} \leq (h + 1) v_{fj(h + 1)} \\+(h + 3) v_{fj(h + 3)}+(h + 5) v_{fj(h + 5)} \quad h={7}, \\ \forall f \in F\setminus\{virtual\},\forall j \in PP \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} 0 \leq v_{fj(h-1)}-v_{fjh}+v_{fj(h + 1)} \leq1 \\ \quad \forall f \in F\setminus\{virtual\},\forall j \in PP, \forall h \in H \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} 0 \leq h v_{fjh} + \left( h + 1\right) v_{fj(h + 1)} \leq 1 \\ \quad \forall f \in F\setminus\{virtual\},\forall j \in PP, \forall h \in H \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{f \in F} v_{fjh} \leq \frac{1}{3} \sum\limits_{f\in F \setminus\{virtual\}} z_{fj} \\ \quad \forall h =\{7,9,11\} \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} v_{fjh}+x^{p}_{ifjh} \leq 1 \quad \forall p \in P,\forall \in I^{p},\\ \forall f \in F\setminus\{virtual\},\forall j \in PP, \forall h = \{7,8,9,10,11,12\} \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{f\in F}\sum\limits_{j\in PP}\sum\limits_{h\in H} x^{p}_{ifjh} = {y^{p}_{i}} \\ \quad\forall i \in I^{p}, \forall p \in P \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} \begin{array}{lllllllllll} \sum\limits_{p\in P}\sum\limits_{i\in I^{p}}\sum\limits_{h\in H} x^{p}_{ifjh} = \tau_{fj} +\sigma_{fj} +\iota_{fj} \\ \quad\forall f\in F\setminus\{virtual\}, \forall \in PP \end{array} \end{array} $$
$$\begin{array}{@{}rcl@{}} x^{p}_{ifjh},{y^{p}_{i}},z_{fjh},v_{fjh} \in \{0,1\} \end{array} $$
$$\begin{array}{@{}rcl@{}} \tau_{fj},\sigma_{fj}, \iota_{fj} \in \mathbb{N} \end{array} $$

Appendix D: Outline of the procedure to generate cancellations and absences

Fig. 6
figure 6

Simulation of patient cancellations

Fig. 7
figure 7

Simulation of nurse absences

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Benzaid, M., Lahrichi, N. & Rousseau, LM. Chemotherapy appointment scheduling and daily outpatient–nurse assignment. Health Care Manag Sci 23, 34–50 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: